Behind the facade of White House happy talk, President Reagan is said to be distressed at poll findings that a solid majority of Americans believe that former national security adviser John M. Poindexter is lying when he says he approved diversion of Iran arms sales profits to the contras on his own.

That is also the president's story, and Reagan is accustomed to being believed. The Iran-contra affair revealed shocking flaws of policy and process, but Reagan's friends say he is more concerned about the damage inflicted on his reputation for truthfulness.

The irony of the president's predicament is that this longstanding and carefully cultivated reputation has become dependent on Rear Adm. Poindexter, the least credible participant in the scandal. Reagan did not plan it this way. He naively expected to be believed when he described himself as a "White House source" in a nationally televised speech last Nov. 13 and wrongly asserted that the Iran initiative was not a trade of U.S. arms for American hostages.

Reagan has often rescued himself with speeches, but this time the public did not believe his story. Nor did they believe him after the Tower board report, which forced Reagan into a backhanded admission that he had actually swapped arms for hostages. When former CIA director William J. Casey died, the president's claim that he had not been informed of the diversion became dependent on Poindexter, portrayed by Secretary of State George P. Shultz as both a weak reed and a deceiver.

Poindexter's loss of credibility did not begin during his five days of sworn testimony at the Iran-contra hearings, where on 184 occasions he responded to questions by answering "I can't recall" or "I don't remember." It was an amazing performance for an admiral whose naval fitness reports described a "photographic memory," and it left even loyal Republican defenders of the president shaking their heads in astonishment.

But those who had worked with Poindexter or been victimized by him were not surprised. Former White House spokesman Larry Speakes, who tried to draw a careful line between stonewalling and lying, learned Poindexter's method of operation the hard way on the eve of the Oct. 25, 1983, invasion of Grenada. A deputy of Speakes had seen a CBS report from Barbados about the forthcoming invasion and called Poindexter about it. "Preposterous," Poindexter replied. "Knock it down hard."

Later, when Speakes challenged Poindexter about his statement, the admiral took refuge in a technicality. He claimed he had been asked about an invasion that already was in progress rather than one about to take place. This claim is also disputed, but Speakes learned from the incident. On Nov. 4, 1986, when the American press was struggling with the first reports of the Iran arms sales, Speakes made it known that Poindexter was the author of a misleading statement issued on Air Force One that said, "As long as Iran advocates the use of terrorism, the U.S. arms embargo will continue."

Lt. Col. Oliver L. North, the fired national security aide, at least freely acknowledged that he lied, even if he seemed to think he deserved a medal for doing it. Poindexter played word games with the American people, insulting their intelligence in his testimony as casually as his conduct in office affronted the Constitution.

"I must tell you that I find it troubling when you say that 'I withheld information from Congress but I did not mislead it,' " Sen. William S. Cohen (R-Maine) said to Poindexter. Brent Scowcroft, a former national security adviser who cares about process, said the testimony reflected "a contempt for procedure" and an unwillingness to "protect the president from himself and crazy people around him." Shultz said Poindexter and Casey tried to use Reagan's communicative skills "to bail them out."

Poindexter did not provide the "smoking gun" that Reagan's foes had sought. But he did something perhaps as damaging, which was to leave the president's reputation resting on the word of a man who simply cannot be believed. Those who study the affair will long wonder why Reagan, on the day he accepted Poindexter's resignation, didn't care enough to ask what had been going on.

Reaganism of the Week: Speaking to state and local officials last Wednesday, the president said: "I have just come from a session with some of the scientists who are working on superconductivity. And now that I'm an authority after 15 or 20 minutes with them, I may change my subject."